When Gretty Amaya took an unpaid maternity leave five months ago, she started what she calls a part-time job to help pay the bills. Ms. Amaya, who lives in Miami, has made more than $2,000 so far by pumping breast milk and selling what is left over after feeding her baby daughter.

Frozen milk from Ms. Amaya — and from hundreds of other women throughout the country — is flown here to what resembles a pharmaceutical factory. Inside, it is concentrated into a high-protein product fed to extremely premature babies in neonatal intensive care units, at a cost of thousands of dollars a baby…..